Then I figured since I was the only mathematician here, I’d go with “Math!” No dice. P. Z. Myers beat me to it.

Well,I’m sticking with math. But let’s make it more concrete. I want people to understand that there is no law of averages. There are no laws of probability (at least not if you mean something like “Really improbable things don’t happen”). You can’t prove just anything with statistics. Math and music actually aren’t that closely related. Math and arithmetic are not the same thing. And, oh yes, in the Monty Hall Problem you double your chances of winning by switching doors.

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On the one hand people believe in the law of averages (e.g. if the wheel’s come up black five times in a row, red is overdue), and on the other hand they readily believe in illusory clustering phenomena (jinxes, hot streaks, trouble always coming in threes). If we could only convince them that these two effects completely cancel one another out, that might acceptably simulate sensible thinking about probability… or maybe not…

My answer: genetic relationism. That there are no genes for “intelligence” or “obesity” and that genes only have relevance in the context of environmental cues. It makes me insane how often journalists get that wrong in science reporting.

Evolution indeed! Part of the problem with teaching evolution these days is that few biologists/etc have a good grasp on the ethical implications that seem to follow the evolutionary world-view. Creationists/ID proponents have leveraged that lack of ethics (or ‘meaning’ in life) to sway public opinion mightily. The facts of evolution are overwhelming, but they are not enough if people 1) are afraid to acknowledge them, or 2) have no way to interpret them in terms of their own world-view.

I’ll be working on a course in June called “Ethics, Education,
and the Evolution Debate” where we hope to get into the ethics involved in this important scientific and public issue. If anyone has ideas for the course, let me know… We’ll also be creating an online version for the fall so that people country/world-wide can sign up.

Yes, Innumeracy is very good. John Allen Paulos has written other books as well on the topic, including A Mathematician Reads the Newspaper, in which he discusses how a familiarity with statistics is helpful when confronting the news of the world.

Justin Whitaker:
I am not a scientist; I’m an English teacher. But I have used the “evolution debate” in my critical thinking classes. What books are you thinking of using in your course? One that looks good to me is Evolution vs. Creationism: An Introduction, by Eugenie Scott.

One of the things I try to get across to my students is that an evolutionist is not devoid of ethics or morality just because he or she disagrees with the concept of creationism (or it’s new moniker, intelligent design).

it seems trite, but I’m convinced that the important thing is to “learn how to learn and think critically about what you learn”. to that end, math clearly is a critical component if it’s taught right. unfortunately, I have no idea how to do that. the way I was taught through undergrad school 40-ish years ago wasn’t right and the way I was taught in grad school was. but since starting kids with graduate level math courses isn’t a super practical approach, that’s not helpful input.

I’m curious why you say the are “no laws of probability”. as far as I know, WLLN, SLLN, CLT, et al are pretty well established, so I assume you are alluding to some folk “wisdom”. in which case I’d just generalize to “don’t speak authoritatively on topics about which you are essentially ignorant”.

somewhat OT:

in your post and comments on the MHP I didn’t see an explanation for the answer that was based on a formally correct solution, was succinct, and seemed easily grasped by non-specialists. here is my cut at a formal solution and a verbal translation which seems succinct and clear to me, although being steeped in probability theory it’s hard for me to judge.

formal solution:

There are two relevant random variables: the car is behind the door you choose first (D1) and the car is behind the door remaining after your and monty’s choices (D2).

P{D2=C}=P{D2=C|D1=C)P{D1=C}+P{D2=C|D1!=C)P{D1!=C}.

since P{D2=C|D1=C}=0 and P{D2=C|D1!=C}=1, P(D2=C)=P(D1!=C)=2/3.

translation:

you and monty each pick a door. if the car is behind your door, it clearly can’t be behind the third door. monty intentionally chooses a door that it isn’t behind, so if it isn’t behind your door it must be behind the third door. hence, the odds that the car is behind the third door are the same as the odds that it isn’t behind your door, ie, 2-in-3.

Oops, I made a bad mistake for an English teacher. I used the wrong “its” in the above comment. There should be no apostrophe, and I wanted to point that out before somebody else does and calls me an idiot. 🙂

You pick Door #1. It’s probably the wrong door. The car is probably behind one of the other two doors. When Monty shows you the goat behind Door #2, then the car is probably behind Door #3 because we have already established that the car is probably NOT behind Door #1.

This common sense explanation seems clear to me. You have a better chance of winning the car if you switch from Door #1 to Door #3.

Okay, but now I have a question. It is stipulated that Monty KNOWS where the car is before he opens Door #2. I have read in some explanations of the MHP that the probablity changes if Monty DOES NOT know where the car is. In this scenario, you pick Door #1. Monty picks Door #2, not knowing where the car is, and reveals a goat. I have read somewhere that in this case – Monty NOT knowing – that your chances DO NOT improve with switching. How can that be? The results of Monty’s actions are the same. This is where I get confused.

The explanation of the Monty Hall problem by ctw (the first one) is based on elementary Bayesian probability; while this may not be the most understandable (for most people) way to formulate an answer, it shows the power that probability can have over our intuition.
In addition, you might be interested to know that most spam filters, search engines (Google, Yahoo!, etc.) rely on Bayesian statistics to filter results.

plus two essays:
Barbour, ‘Ways of Relating Science and Religion’ and
Barbour, ‘Theological Issues in Evolution’

The ethics issue goes beyond the denial of creation/ID in evolution. In reading someone like Dawkins especially one can be made to feel as though all ethical (and of course religious) notions are so much silliness. Dennett comes close to this, but still gestures meekly toward morality surviving the ‘universal acid’ of evolutionism. Ruse, an agnostic, and Miller, a Catholic, hold the middle ground, raising good questions about the nature of science itself. Behe is smart, and lucidly presents the claims of the ID theorists.

Justin:
Richard Dawkins might very well think that religion is silly, but he does not think that ethics are silly. He thinks that religion is an impediment to acting ethically. It is a misconception that atheists care not about ethics and morality. Dawkins argues that atheists are usually more ethical and moral than believers. I’m not trying to put words in Dawkins’s mouth. There’s plenty online about this. Read some of the stuff Dawkins has to say on the subject.

Dawkins was once asked, “How would we be better off without religion?” This is how he responded:

We’d all be freed to concentrate on the only life we are ever going to have. We’d be free to exult in the privilege — the remarkable good fortune — that each one of us enjoys through having been being born. An astronomically overwhelming majority of the people who could be born never will be. You are one of the tiny minority whose number came up. Be thankful that you have a life, and forsake your vain and presumptuous desire for a second one. The world would be a better place if we all had this positive attitude to life. It would also be a better place if morality was all about doing good to others and refraining from hurting them, rather than religion’s morbid obsession with private sin and the evils of sexual enjoyment.

I could go on and on about Dawkins. I admire his genius and his tenacity, but still remember his fumbling/bumbling answer when a BBC interviewer just a couple years ago asked him, “what does it mean to you that your daughter loves you?”

Dawkins, in “The Selfish Gene” writes: “The argument of this book is that we, and all other animals, are machines created by our genes.” (Ch1) He goes on to repeatedly reduce humans to ‘gene machines;’ you and I are just what our clever genes have slopped together to best replicate themselves.

Our religious beliefs, or moral conditionings, and even Darwin’s theory (see CH 11), are then reduced to memes. Memes are analogous to genes, and any scientist will tell you it is rediculous to talk about ‘good’ and ‘bad’ genes – we can only talk of those that replicate more or less, adapt more quickly or slowly, etc. Genes are not normative, and by implication, neither are memes.

While Dawkins is happy to argue for his particular memes, by his own theory, he cannot say one is better. Math and science, he must say, are simply very, very useful memes. This is what philosophers call a deflationary theory of truth. This ‘universal acid’ (as Dennett calls evolutionary theory) cannot be restricted to religion alone; it eats through our ethics, our science, and even our daughter’s love.

Justin:
I realize that this discussion may be pointless, but I am sure that Dawkins loves his daughter. He’s a human being with emotions, just like you and me. But from a scientific stance, he might just be right. That doesn’t mean that I am going to stop loving my family. Human beings are complex creatures. I am sure we are far from knowing all the answers.

I just thought I’d follow up on my previous comment with this quote from the first chapter of Dawkins’s book The Selfish Gene:

I am not advocating a morality based on evolution. I am saying how things have evolved. I am not saying how we humans morally ought to behave. I stress this, because I know I am in danger of being misunderstood by those people, all too numerous, who cannot distinguish a statement of belief in what is the case from an advocacy of what ought to be the case.

I think the discussion is actually very important; and you bring out the key point, which is the tension between our being humans (having emotions, etc) and the scientific stance, where much of what being a human is all about seems to fall out of the picture. It is reduced to, and arguably always eliminated by, lower level processes.

The difficult question is how do we move logically and consistently from the stance where we are ‘gene machines’ to the one where we are loving, caring human individuals? Obviously there is a connection between ‘what is the case’ and ‘what ought to be the case’.

I am no expert, of course, but from what I have read on the subject, emotions such as love and caring seem to be “by-products” of our evolutionary journey. By-products or not, they are still important parts of our make-up. They are, it could be argued, what makes us “human.” Human beings are the way they are because of natural selection. It seems reasonable to me that we have developed these altruistic traits through completely natural means. And since there is absolutely no verifiable evidence of a supernatural hand in our development, why assume there is such a guiding hand? Because it makes us feel better?

I think you’re quite in line with the contemporary (metaphysical) naturalistic thought. The problem with metaphysical naturalism is that it is either incomplete in the sense that it leaves out ethics while purporting to give a complete description of humanity, or it explicitly denies the reality of ethical notions. Certainly we are the way we are because of evolution, but this includes our negative tendencies as well as our good ones (e.g. activities such as rape can be explained evolutionarily, but it is very difficult, as with Dawkins’ loving daughter, to give a clear ethical account, that is, why rape is wrong, from an evolutionary standpoint – that’s not to say it is impossible, just difficult).

Perhaps we could say that some scientists, their efforts to be morally neutral, have become morally blind. THAT, I would argue, is the heart of the difficulty with getting the public to embrace evolutionary theory and science in general. To make evolution meaningful to the public, we who study it must fully grasp its ethical implications, and, if necessary, its shortcomings.

Who is denying the reality of ethical notions? Isn’t it self-evident that human beings have notions about what is right and what is wrong, regardless of how those notions came to be? To say that our ethical notions are the result of natural selection is not to disparage them or diminish their importance. One need not buy into supernatural hocus pocus to affirm that we need ethical guidelines. I am reminded of Thomas Jefferson who, while denying that Jesus Christ was divine, and even once remarking that belief in the Holy Trinity was “metaphysical insanity,” did not hesitate to say that Jesus was “the greatest teacher of moral truths that ever lived,” and that He provided us with “the most sublime and benevolent code of morals which has ever been offered to man.”